Where does the work come from if tidal forces are stretching elastic objects? An elastic object e.g. a rubber band will be stretched


*

*in accelerated expanding FRW-spacetime

*during radial free fall in Schwarzschild spacetime
by tidal forces due to Ricci- and Weyl-curvature resp., until equilibrium with its internal cohesive forces is achieved. 


The work done to stretch the rubberband is represented by the elastic potential energy stored in it. 
Where does this work done come from in these two cases?
 A: In the case of a rubberband falling into a Schwarzschild blackhole, the work comes from the increasing differential in binding energy between the two ends of the string. This is completely analaguous to the Newtonian case. Binding energy is well defined due to the existence of a time translation symmetry (i.e. timelike Killing field.)
The situation in FRW is slightly different. The rubberband in an FRW metric will only expand if 


*

*The expansion of the of the FRW spacetime is accelerating


or


*The intitial conditions of the rubberband are such that there is relative kinetic energy between the two ends of the rubberband.


If neither is the case the size of the rubberband will just stay the same, and no work is done.
In case 1, the work comes from the vacuum energy and effectively slows down the acceleration. Instead of a rubber band it is easier to think about an FRW metric filled with an elastic medium. The effect is that you get an FRW solution with a slightly different equation of state (the pressure is a bit larger).
In case 2, the work simply comes from the relative kinetic energy of the opposite ends. This slows down the expansion of the rubber band.
